The Jesuits (the Society of Jesus) are an organization of Catholic priests founded by Saint Ignatius Loyola and his companions in the early sixteenth century. They were and are thus part of the Catholic church and have been through the centuries a highly influential faction within it, and frequently a controversial one. The Jesuits have attained their level of influence for a variety of reasons. Some of them are as follows: a powerful set of spiritual insights inculcated in the members through the Spiritual Exercises of Saint Ignatius; a highly effective, streamlined, flexible organizational structure embodied in their so-called Constitutions; a cultivation of learning in diverse fields including theology but extending to the humanities and sciences; a dedication to education and schooling that has helped them develop connections to persons of influence in numerous fields of human endeavor; an active engagement with and dedication to the "unchurched" world, which brought them to the colonial missions in the sixteenth century and keeps them engaged with the secular world and its ideas today. In conclusion it is worth reiterating that the Jesuits are not "different from the Catholic church". Even through they are different from parts of the Catholic church and factions within the church have opposed ideas and tactics that have guided the Jesuit order, the order itself is an integral part of church. Most recently Pope Benedict remarked in an address to the Jesuits: "the Church needs you, relies on you and continues to turn to you with trust, particularly to reach those physical and spiritual places which others do not reach or have difficulty reaching."
Early history: J W O'Malley, The First Jesuits.
Papal Address: http://www.jesuitvocations.org.uk/pope-benedict--xvi-addresses-the-jesuits/